document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=469718>Question 469718</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A woman is standing on a hill looking at a flag pole known to be 36 feet tall. If she measures 18&#9702; angle to the top of<BR>\n" );
document.write( "the flag pole and a 14&#9702; angle to the bottom of the flag pole as shown, how far away is she standing from the flag pole? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #322237 by </B><A HREF=/tutors/aboutme.mpl?userid=ccs2011><B>ccs2011(207)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ccs2011><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ccs2011><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=322237\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Draw 3 lines from the woman to the flag pole , one to the top, one to the bottom and one straight across perpendicular to flag pole.<BR>\n" );
document.write( "This forms 2 right triangles.<BR>\n" );
document.write( "Angle opposite flag pole in top triangle is 18 degrees<BR>\n" );
document.write( "Angle opposite flag pole in bottom triangle is 14 degrees<BR>\n" );
document.write( "The adjacent side for both angles is the distance from the flag pole, call it d.<BR>\n" );
document.write( "Let the length of the top part of flag pole be x, then length of bottom part is 36-x.<BR>\n" );
document.write( "In this way their sum equals 36, the length of the flag pole.<BR>\n" );
document.write( "Use trig relationships to solve for d<BR>\n" );
document.write( "Note that tan(theta) = opp/adj<BR>\n" );
document.write( "Thus<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%2818%29+=+x%2Fd ALIGN=MIDDLE  ALT=\"tan%2818%29+=+x%2Fd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%2814%29+=+%2836-x%29%2Fd ALIGN=MIDDLE  ALT=\"tan%2814%29+=+%2836-x%29%2Fd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve for x in 1st equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+d%2Atan%2818%29 ALIGN=MIDDLE  ALT=\"x+=+d%2Atan%2818%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute this in for x in 2nd equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%2814%29+=+%2836+-+d%2Atan%2818%29%29%2Fd ALIGN=MIDDLE  ALT=\"tan%2814%29+=+%2836+-+d%2Atan%2818%29%29%2Fd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve for d:<BR>\n" );
document.write( "Multiply by d on both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Atan%2814%29+=+36+-+d%2Atan%2818%29 ALIGN=MIDDLE  ALT=\"d%2Atan%2814%29+=+36+-+d%2Atan%2818%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add d*tan(18) on both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Atan%2814%29+%2B+d%2Atan%2818%29+=+36 ALIGN=MIDDLE  ALT=\"d%2Atan%2814%29+%2B+d%2Atan%2818%29+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factor d from left side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%28tan%2814%29%2Btan%2818%29%29+=+36 ALIGN=MIDDLE  ALT=\"d%28tan%2814%29%2Btan%2818%29%29+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide by tan(14)+tan(18) on both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+36%2F%28tan%2814%29%2Btan%2818%29%29 ALIGN=MIDDLE  ALT=\"d+=+36%2F%28tan%2814%29%2Btan%2818%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using scientific calculator<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+62.69 ALIGN=MIDDLE  ALT=\"d+=+62.69\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Therefore the woman is approximately 62.7 ft away from the flag pole. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );